Voltage-variable capacitor with increased current conducting perimeter

ABSTRACT

A parallel-plate, voltage-variable capacitor is designed to have an increased current conducting perimeter relative to its area. In one approach, the perimeter is increased by changing the shape of the plates. In another approach, the varactor is implemented by a number of disjoint plates, which are coupled in parallel.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application is a continuation of U.S. patent applicationSer. No. 10/144,185, “Voltage-Variable Capacitor with Increased CurrentConducting Perimeter,” by Robert A. York, filed May 10, 2002; whichclaims priority under 35 U.S.C. § 119(e) to U.S. Provisional PatentApplication Serial No. 60/337,364, “Ferroelectric Varactor Design,” byRobert A. York, filed Dec. 5, 2001. The subject matter of all of theforegoing is incorporated herein by reference in its entirety.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] This invention generally relates to voltage-variable capacitors(varactors) of a parallel plate design.

[0004] 2. Description of the Related Art

[0005] Capacitors are a basic building block for electronic circuits andvoltage-variable capacitors (varactors) have the added flexibility thattheir capacitance can be tuned by changing a bias voltage across thecapacitor. Dielectric materials which have a permittivity that dependson the applied electric field can be used to form such varactors.Varactors have an added advantage that they can be easily integratedwith other components, particularly if the dielectric layer is a thinfilm. One common approach to voltage-variable varactors is the“parallel-plate” configuration, in which the voltage-variable dielectricis sandwiched between two electrodes. For example, in an integratedvaractor, one electrode may be a bottom conducting layer, the dielectricmay be a ferroelectric thin film deposited over the bottom electrode,and the top electrode may be a metal layer.

[0006] In the parallel-plate configuration, the capacitance of thevaractor is determined in part by the area of overlap of the topelectrode, the dielectric layer and bottom electrode. For convenience,this area shall be referred to as the active region of the varactor. Inmany designs, the active region is determined mainly by the size andshape of the two electrodes; the dielectric layer is made large enoughso that it does not additionally limit the active region. Thus, thevaractor is designed for a specific capacitance by adjusting the lateraldimensions of the top and/or bottom electrodes. The active regiontypically is square-shaped (or close to square-shaped) although othershapes, including circular, may also be used.

[0007] The electrodes have some finite resistance. This resistance leadsto loss and also limits the operating bandwidth of the varactor. Forexample, the electrode resistance in series with the varactor'scapacitance forms an RC combination with a certain time constant. Higherresistance means longer RC time constant and lower cutoff frequency. Theresistance typically is reduced by increasing the thickness of the metalfilms forming the electrodes. However, limitations in the fabricationprocess can place an upper limit on the maximum thickness of theelectrodes. Increasing the thickness of the electrodes can also becostly since, for various reasons, the bottom electrode may be made froman expensive refractory metal such as platinum, palladium, iridium andrelated compounds. For these reasons, the electrode thicknesses areconstrained. This, in turn, limits the sheet resistance and the currenthandling capacity of the varactor as a result of effects such aselectromigration and/or Joule-heating. Hence, the conventionalparallel-plate design is not particularly well suited for implementinglow-loss, high-current varactors.

SUMMARY OF THE INVENTION

[0008] The present invention overcomes the limitations of the relatedart by providing a parallel-plate varactor in which the currentconducting perimeter of the active region for at least one electrode isincreased relative to the area of the active region. The currentconducting perimeter is that portion of the geometrical perimeter whichsupports current flow between the active region and the rest of theelectrode. In one approach, the current conducting perimeter isincreased by changing the shape of the active region, for example byusing a long skinny active region rather than a square one. In anotherapproach, the active region is implemented by a number of disjointsubregions, termed “cells,” which are coupled in parallel. The cellstogether have the area required to implement a certain capacitance butsubdividing the active region into cells increases the total currentconducting perimeter.

[0009] Increasing the current conducting perimeter addresses theproblems with conventional parallel-plate designs. The increasedperimeter results in more paths for current to move between thedielectric layer and the bulk regions of the electrodes, thus reducingthe resistance of the electrodes. This same effect also increases thecurrent handling capacity of the varactor. Furthermore, these gains areachieved without having to increase the electrode thickness, althoughdoing so may result in even further gains.

[0010] In one implementation, a parallel plate varactor includes abottom electrode, a top electrode and a dielectric layer sandwichedbetween the top electrode and the bottom electrode. The permittivity ofthe dielectric layer varies according to an electric field applied tothe dielectric layer. The active region of the varactor is defined by anoverlap between the top electrode, the dielectric layer and the bottomelectrode. For at least one of the electrodes, the resistance of theactive region of the electrode is significantly higher than a resistanceof a bulk region of the electrode. Furthermore, the active region has alateral area A, the electrode has a current conducting perimeter P, anda ratio R of the perimeter P to a square root of the area A is at least2.0.

[0011] In one embodiment, the dielectric layer is a voltage-variablethin film (e.g., based on a ferroelectric material) and the highresistance electrode is a refractory metal. Examples of voltage-variableferroelectric thin films include barium titanate, strontium titanate andbarium strontium titanate. Examples of refractory metals includeplatinum, palladium, iridium, nickel, tungsten, or ruthenium.

[0012] In one particular aspect of the invention, the active regionincludes one or more rectangular cells. The active region of the bottomelectrode has a higher sheet resistance than the active region of thetop electrode. For example, platinum may be used for the bottomelectrode, barium strontium titanate as the dielectric layer and goldfor the top electrode. Furthermore, for each cell, the currentconducting perimeter of the bottom electrode includes at least threesides of the cell and the current conducting perimeter of the topelectrode includes the fourth side of the cell.

BRIEF DESCRIPTION OF THE DRAWING

[0013] The invention has other advantages and features which will bemore readily apparent from the following detailed description of theinvention and the appended claims, when taken in conjunction with theaccompanying drawing, in which:

[0014]FIGS. 1A and 1B are a top view and cross-sectional view,respectively, of a varactor according to the present invention.

[0015]FIG. 2 is a top view of an active region having multiple cells.

[0016]FIG. 3 is a top view of another varactor having multiple cells.

[0017]FIGS. 4A-4C are top view and cross-sectional view pairs,illustrating fabrication of one cell of the varactor of FIG. 3.

[0018]FIG. 5 is a diagram of a resistive model for the cell of FIG. 3.

[0019]FIG. 6 is a graph of cutoff frequency for the varactor of FIG. 3as a function of capacitance and of number N of cells.

[0020]FIGS. 7A and 7B are graphs of excess current conducting perimeteras a function of electrode length for N=1 and N=4 cells, respectively.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0021]FIGS. 1A and 1B are a top view and cross-sectional view,respectively, of a voltage-variable capacitor (varactor) 100 accordingto the present invention. The varactor 100 includes a bottom electrode110, a top electrode 140 and a layer 120 of dielectric materialsandwiched between the top electrode and the bottom electrode. The topelectrode 140, the dielectric layer 120 and the bottom electrode 110form a parallel plate capacitor. The active region 150 of the capacitoris defined by the overlap between the top electrode 140, the dielectriclayer 120 and the bottom electrode 110. The varactor 100 in FIG. 1 isdrawn with a specific shape for the electrodes 110, 140, dielectriclayer 120 and active region 150. However, this is not meant as alimitation. FIG. 1 is intended to be a general depiction of a varactor100 with electrodes 110, 140, dielectric layer 120 and active region150. Furthermore, varactor 100 shows the most relevant layers 110, 120,140, but this is not meant to imply that other layers do not exist. Forexample, additional layers located between those shown may be used forvarious purposes according to conventional techniques. Examples includelayers to increase adhesion, to provide a diffusion barrier, or toimprove the Schottky barrier height.

[0022] The dielectric layer 120 is voltage-variable in the sense thatthe dielectric material has a field-dependent electrical permittivity.Thus, the capacitance of the varactor can be changed by changing thevoltage applied across the dielectric layer 120. By changing the voltageapplied across the two electrodes 110,140, the electric field within thedielectric layer 120 is also changed. This, in turn, changes thedielectric constant of the dielectric layer 120, thus changing thecapacitance of the varactor. 100. This invention is not specific to aparticular choice of dielectric material or film thickness orfabrication sequence. Examples of dielectric materials includeferroelectric materials. The dielectric layer 120 preferably exhibits afield-dependent permittivity in a (non-hysteretic) paraelectric stateover a useful temperature range (e.g., −30 C to +90 C).

[0023] Two factors which can limit the performance of a varactor are theresistance of the varactor and the current handling capacity of thevaractor. Higher resistance results in higher ohmic losses and alsoresults in a lower operating bandwidth (e.g., due to a longer RC timeconstant). Lower current handling capacity limits the applications inwhich a varactor can be used.

[0024] In addition to the active region 150, electrodes also have a“bulk” region, which is the portion of the electrode away from theactive region. Typically, the resistance of the bulk region isrelatively insignificant relative to that of the active region. Forexample, if an electrode is narrow in the active region and then opensup into a wide area (e.g., a bonding pad), the wide area is part of thebulk region of the electrode and typically will have minimal resistancecompared to the narrow portion.

[0025] In varactor 100, the active region of one or both electrodes 110,140 has a resistance that is significantly higher than the resistance ofthe bulk region of the electrode 110, 140. For example, the activeregion of the electrode may be thinner than the bulk region or it may bemade from a different material with lower conductivity. In both of theseexamples, the sheet resistance of the active region is significantlyhigher than that of the bulk region and, therefore, the overallresistance is also higher. Alternately, the active region and bulkregion may have a similar sheet resistance but the lateral geometrycauses the active region to have a significantly higher resistancecompared to the bulk region. In any event, in varactor 100, the activeregion of the high-resistance electrode is a significant, if notdominant, contributor to the overall resistance of the varactor,resulting in the unwanted effects described previously.

[0026] Varactor 100 reduces these effects by increasing the “currentconducting” perimeter of the active region 150 relative to the area ofthe active region. The “current conducting” perimeter is that portion ofthe perimeter which supports current flow between the active region andthe rest of the electrode. For example, referring to electrode 110 inFIG. 1, the geometrical perimeter includes sides 152A-D. However, thecurrent conducting perimeter only includes sides 152B-D and not side152A. This is because, for electrode 110, current can flow from theactive region 150 through sides 152B, C or D to the bulk of theelectrode. However, there is no current path from the active regionthrough side 152A.

[0027] Increasing the current conducting perimeter increases the numberof current paths between the active region and the bulk of theelectrode. The increased current conducting perimeter results in lessresistance through the high resistance electrode (assumed to beelectrode 110 in the above example) and therefore less resistanceoverall since the high resistance electrode makes a significantcontribution to the overall resistance. The increased perimeter alsoresults in better current handling capacity. The current conductingperimeter can be increased in a number of different ways and this effectcan be quantified using a number of different measures.

[0028] In one approach, the effect is quantified by the ratio

R=P/sqrt(A)   (1)

[0029] where P is the current conducting perimeter of the active region,A is the lateral area of the active region and sqrt( ) is the squareroot operator. For a square electrode in which the current conductingperimeter is one half of the geometrical perimeter, the ratio R=2.0. Forcomparison, a rectangular active region with a 2:1 aspect ratio in whichhalf of the geometrical perimeter is current conducting has a ratio R=3/sqrt(2)=2.13. A circular active region with 50% conducting perimeterhas a ratio R=sqrt(π)=1.77. A square active region with three sidesconducting has a ratio R=3.

[0030] One way to increase the current conducting perimeter forrectangular shaped active regions (assuming that the fraction of thegeometrical perimeter that is current conducting remains constant) is toincrease the aspect ratio of the rectangle. The use of long, narrowelectrodes (and active regions) results in an increased perimetercompared to a more square shaped active region of the same area.

[0031] This effect is even more pronounced if the fraction of thegeometrical perimeter that is current conducting also increases as theaspect ratio increases. For example, in one approach, two long sides andone short side of the rectangular active region are current conducting.The ratio R for this type of rectangular active region with aspect ratiom (i.e., the active region is L×mL where L is some length, m≧1) is givenby

R=(2m+1)/sqrt(m)   (2)

[0032] This function has a minimum at m=1 (i.e., square shaped activeregion) and increases with increasing m.

[0033] The active region can have shapes other than rectangular. Forexample, circular or disc-shaped active regions are sometimes used.However, rectangular active regions are generally easier to lay out andmanufacture. In addition, they typically have more current conductingperimeter than a circular or disc-shaped active region of equal area.

[0034] Another way to increase the perimeter of an active region is toimplement the active region as a number of disjoint subregions, whichshall be referred to as cells. FIG. 2 is a top view of an active region150 having N cells 250A-N. Each cell 250 behaves as a “mini varactor”and the multiple mini varactors are coupled in parallel to form theoverall varactor. An active region made up of multiple cells generallywill have a higher R ratio than a comparable active region made up of asingle cell.

[0035] For example, assume that a one cell design has an area A, currentconducting perimeter P and capacitance C. The corresponding R=P/sqrt(A).All else being equal, the capacitance C is directly proportional to thearea A. Now assume that the capacitance C is implemented as an activeregion having N cells, each of which is the same shape and design as theoriginal cell. Each cell is a 1/sqrt(N) scaled version of the originalcell. Therefore, each cell has an area of A/N and a current conductingperimeter of P/sqrt(N). The total area for all N cells is A (andtherefore the capacitance is the same as for the one cell design) andthe total current conducting perimeter is P sqrt(N). The correspondingR=sqrt(N) P/sqrt(A). In other words,

R(N)=sqrt(N)R(1)   (3)

[0036] where R(1) is the R ratio for the one cell design and R(N) is theR ratio for the N cell design. The R ratio has been increased by afactor of sqrt(N) by moving from a one cell active region to an N cellactive region.

[0037] Both principles discussed above may be applied to a given design,although at times tradeoffs between the two may be required. Forexample, consider the design of a varactor with an active region of areaL², L>1. Assume that the minimum feature size is 1. Table 1 shows fourpossible designs for this varactor, listed in increasing order of Rratio. In all of the designs, the cells are rectangular in shape and itis assumed that two long sides and one short side of each cell iscurrent conducting. TABLE 1 Four Designs for a Varactor of Area L² TotalCurrent Conducting Active Region Total Area Perimeter R Ratio 1 cell ofL² 3 L 3 dimension L × L 1 cell of L² (2 L² + 1) 2 L + 1/L dimension L²× 1 L cells of L² L(2 L + 1) 2 L + 1 dimension L × 1. L² cells of L² 3L² 3 L dimension 1 × 1.

[0038] Table 1 is consistent with the general notion that it ispreferable to have a larger number of cells, even if they are square inshape. The number of cells, however, can be constrained by otherfactors, for example limits in lithographic capability, current-handlingconsiderations, and materials limitations. For example, in some caseswhere small capacitance values are required, the minimum realizablefeature size may dictate that only single-cell designs are feasible. Inthis case, a long, narrow active region is preferred to an active regionthat is more square in shape. As another example, although long, narrowactive regions are generally preferred, beyond a certain aspect ratio,incremental gains that result from further increasing the aspect ratiomay be offset by other effects, for example increased resistance in theother electrode (i.e., the low resistance electrode). Generallyspeaking, significant gains can be realized by moving from an aspectratio of 1:1 to 2:1, moderate gains for aspect ratios in the range of2:1 to 10:1, and diminishing returns for aspect ratios beyond about10:1. Hence, all other factors being equal, aspect ratios in the rangeof 2:1 to 10:1 are generally preferred.

[0039] In one implementation, the dielectric layer 120 is a thin filmand the entire varactor is integrated on a substrate. Examples ofsuitable voltage-variable thin film materials include barium titanate,strontium titanate, and composites of the two (e.g., barium strontiumtitanate). The materials may also include small concentrations of one ormore dopants to modify certain properties. Standard IC fabricationmethods may be used to fabricate the integrated varactor. To reducecosts, inexpensive insulating substrates are usually preferred,including but not limited to high-resistivity silicon (HR Si),crystalline sapphire (Al₂O₃), aluminum nitride (AlN), quartz and glass.These substrates are polished for low surface roughness forcompatibility with growth of smooth ferroelectric films with highbreakdown fields. This approach results in low-cost, small size,reliable components which are suitable for mass production and forintegration with other circuit elements.

[0040] Thin-film varactors can be used in a variety of applications suchas radio-frequency (RF) or wireless electronics, voltage-controlledoscillators, impedance matching networks, tunable filters, and numerousother applications. A thin-film varactor is attractive because it can beeasily integrated alongside other active and passive electricalcomponents on many different host substrates, including semiconductors(such as silicon, gallium arsenide, silicon carbide, gallium nitride,etc.) and insulators (such as glass, quartz, sapphire, etc.). However,thin-film ferroelectric materials have a high intrinsic capacitancedensity, which means that typical capacitance values for RF circuitdesigns will be realized by small active regions. In addition,processing steps for ferroelectric materials can require conditions thatlimit the choice of materials for the electrode(s). High temperatureprocessing may limit electrode materials to those with high meltingpoints which also do not oxidize easily. Examples of such materialsinclude platinum and other refractory metals such as palladium andtungsten, but generally exclude commonly used conductors such as gold,copper and aluminum. Unfortunately, these materials typically havehigher resistivity and can also be quite expensive. This in turn canlead to high ohmic losses and high current densities. Hence, theprinciples described above for reducing resistance and current densitiesare especially suited for these devices.

[0041] As one example, these varactors can be used in RC tuning circuitsfor RF applications, such as mobile phones. While specific numbers willvary by application, 2:1 capacitance variations and capacitances in therange of 0.01 pF to 10 nF are not unheard of. Similarly, DC controlvoltages may be in the range of −100 to +100 volts, depending on thefilm thickness and the specific application. The varactors preferablyare operated at voltages that are less than half their intrinsicbreakdown voltage.

[0042]FIG. 3 is a top view of an example thin-film ferroelectricvaractor 300 having multiple cells 350A-N. In this varactor, theferroelectric layer 120 is a barium strontium titanate (BST) thin film.The bottom electrode has two parts which shall be referred to as thebottom electrode layer 112 and the bottom contact layer 114. These twolayers 112, 114 are in electrical contact with each other. Each layermay include one or more types of materials, although they are shown andwill be described as single layers of material in this example. Theactive region (i.e., each cell 350) is defined by the lateral overlap ofthe bottom electrode layer 112, the BST film 120 and the top electrodelayer 140. The bottom electrode layer 112 is platinum in this examplebecause it must be compatible with BST processing. The bottom contactlayer 114 is a thick metal layer (e.g., gold) that provides electricalconnection with reduced resistance to the bottom electrode layer 1 12.The top electrode 140 could be formed from the same thick metal layer ora separately deposited metal layer. In this example, it is assumed to bethe same gold layer.

[0043] In FIG. 3, the full lateral extent of the top electrode 140 andthe bottom contact layer 114 are visible. The BST film 120 is aneight-sided shape which is partially hidden by top electrode 140. Fiveof the eight sides are fully visible, two of the eight sides arepartially visible and one side is obscured by top electrode 140. Thebottom electrode layer 112 is rectangular in shape but extends beyondwhat is visible in FIG. 3. It is partially hidden by portions of theferroelectric 120, bottom contact layer 114 and top electrode 140.

[0044]FIGS. 4A-4C are pairs of top view and cross-sectional view,illustrating fabrication of one cell 350 of varactor 300. In FIG. 4A,the bottom electrode layer 112 has been deposited on a substrate. Inthis example, layer 112 is a thin layer of platinum. Platinum isselected for compatibility with the BST processing and a thin layer ispreferred since platinum is expensive. The layer 112 contains N disjointsubregions, each corresponding to one of the cells 350. In one approach,platinum is deposited across the entire substrate, the desiredsubregions are then masked, and the material in the unmasked regions areremoved. What remains is the N subregions. In an alternate approach, aliftoff layer is deposited in areas other than the desired subregions,platinum is deposited across the substrate, and removal of the liftofflayer also removes the platinum from the unwanted areas. Otherpatterning techniques may be used.

[0045] In a next step, the BST film 120 is grown on top of the platinumlayer 112. Conventional growth and patterning techniques may be used.Like layer 112, the BST film 120 contains N separate subregions, one foreach cell 350. The film 120 overlaps the electrode layer 112. The resultis shown in FIG. 4B. In the top view, the hidden portions of the bottomelectrode layer 112 are shown by dashed lines.

[0046] In a final step, a gold layer is deposited and patterned to formboth the top electrode 140 and the bottom contact layer 114 as shown inFIG. 4C. In the top view, the dashed lines indicate portions of thelower layers which are hidden by this gold layer. The bottom contactlayer 114 overlaps with the bottom electrode layer 112, thus providingan electrical path to all of the disjoint subregions in layer 112. Thegold layer 114,140 is thicker than the platinum layer 112 and gold is abetter conductor than platinum. As a result, the platinum resistance isa significant, if not dominant, contribution to the overall resistanceof the varactor.

[0047] The cells 350 making up the active region are rectangular inshape with dimension W×L in FIG. 4C. Each of the top electrode 140,bottom electrode layer 112 and BST film 120 entirely overlaps cell 350.Three sides of the cell 350 are defined by the top electrode 140. Thefourth side is defined by the bottom electrode layer 112. The topelectrode 140 and bottom contact layer 114 provide external contacts tothe varactor. For example, they may lead to other circuit components orto external connections, such as bonding pads.

[0048] The top electrode 140 and bottom electrode (layers 112 and 114)preferably are thick and good conductors in order to reduce sheetresistance and current densities. However, in this particular example,bottom electrode layer 1 12 is relatively thin and a poor conductor(i.e., platinum), as a result of processing requirements imposed by theBST layer 120. However, the bottom contact layer 114 is relatively thickand a good conductor (gold). Thus, it is advantageous to place thebottom contact layer 114 in close proximity to the cells 350, in orderto minimize the resistance resulting from the platinum layer 112. Topelectrode 140 is also thick and a good conductor to minimize sheetresistance.

[0049] The use of multiple, narrow top electrodes 140 in close physicalproximity to the bottom contact layer 114 results in a geometry withincreased device perimeter for a given active area and with lowresistance paths from the active region to external contacts. Thisgeometry reduces ohmic losses and current densities in the devicecontacts, thus improving the electrical performance of the varactor. Inparticular, the layers are laid out so that the current conductingperimeter of the platinum layer 112 is relatively large. Two long sidesand one short side of the rectangular active region are currentconducting for a total current conducting perimeter of 2L+W for platinumlayer 112.

[0050]FIG. 5 is a diagram of a resistive model for the cell 350.Resistances in the bulk regions of the bottom contact layer 114 and topelectrode 140 are assumed to be negligible. Assuming that current flowsfrom the top electrode 140 to the bottom contact layer 114, the currentencounters the impedances shown in Table 2. TABLE 2 Impedances in theResistive Model of FIG. 5 Symbol Description Expression R_(access)Resistance from bulk of top electrode R_(access) = r₁d/W 140 to activearea of top electrode R_(top) Average resistance through active areaR_(top) = r₁L/(3 W) of top electrode Z_(varactor) Impedance offerroelectric material Z_(vavactor) = 1/(y_(d)WL) R_(side) Resistancefrom side of active area of R_(side) = r_(b)g/L bottom electrode layer112 to bulk of bottom contact layer 114 R_(end) Resistance from end ofactive area of R_(end) = r_(b)g/W bottom electrode layer 112 to bulk ofbottom contact layer 114

[0051] An approximate expression for the impedance of the cell 350 isthen $\begin{matrix}{Z_{i\quad n} \approx {\underset{\underset{R_{S}}{}}{{\frac{r_{t}}{W}( {d + \frac{L}{3}} )} + {r_{b}\frac{g}{{2L} + W}}} + \frac{1}{y_{d}{WL}}}} & (4)\end{matrix}$

[0052] R_(s) is the equivalent series resistance for the cell. Theseries resistance consists of R_(access) and R_(top) coupled in serieswith the parallel combination of R_(side), R_(end) and R_(side). Theresistance contribution from the bottom electrode layer 112 is usuallythe dominant term due to the materials and thickness differencesdescribed above. Furthermore, this model highlights the importantfeature that the resistance contribution from the bottom electrode layer112 is a direct function of the quantity 2L+W, which is the currentconducting perimeter. Thus, the series resistance of the cell can bereduced by increasing the current conducting perimeter.

[0053] Considering only electrode losses (i.e., assuming g_(d)=0), thecutoff frequency for the cell is given by $\begin{matrix}{f_{c} \approx {\frac{1}{2\quad \pi \quad r_{b}c_{d}g}( \frac{{2L} + W}{A} )}} & (6)\end{matrix}$

[0054] where A is the area of the cell. The cutoff frequency is ameasure of performance. Higher cutoff frequencies are usually preferred.Assuming the series resistance is dominated by the contribution from thebottom electrode layer 112, the cutoff frequency is approximatelyshowing the dependence on the current conducting perimeter and on theperimeter to area ratio. Thus, to realize a varactor with a high cutofffrequency (i.e., a low series resistance), devices with large R ratiosand/or current conducting perimeters are preferred. The R ratio and/orcurrent conducting perimeter can be increased using the techniquesdescribed previously, for example by increasing the aspect ratio of thecells and/or by increasing the number of cells. Note that thecutoff-frequency of N identical capacitors connected in parallel is thesame as that of the individual capacitors. Thus a multiple-contactgeometry like that shown in FIG. 3 can provide low resistive loss andhigh cutoff frequency for a given varactor capacitance.

[0055] For example, if a varactor has N cells, each of which is W×L asshown in FIG. 3, then the total area of the active region will be A=NWL.The N cells are connected in parallel, so the total resistance for thevaractor will be 1/N of the resistance for one cell. Referring to Eqn.4, dividing the expression for the series resistance by N and making useof the equation A=NWL yields a total series resistance of$\begin{matrix}{R_{s} = {{\frac{r_{t}L}{A}( {d + \frac{L}{3}} )} + \frac{r_{b}{gL}}{{2{NL}^{2}} + A}}} & (7)\end{matrix}$

[0056]FIG. 6 is a graph of cutoff frequency for the varactor of FIG. 3as a function of capacitance and of the number N of cells, for N=1, 2,3, and 4. The cells are assumed to be the same shape for all designs. Inthis example, if a 0.2 pF capacitor were desired, FIG. 6 shows that thecutoff frequency can be increased by 75% using a three-cell designinstead of a one-cell design.

[0057] Current handling is another factor that limits the performance ofvaractors. If the electrodes are made from metal films, there are twofailure mechanisms which typically will limit the current densities inthe electrodes. One is electromigration failures, in which momentumtransfer from the mobile charges to the metal atoms is sufficient totear the material apart. The other is Joule heating, in which highcurrent densities create large thermal gradients that degrade the metalor neighboring materials. In each case, the current density J in themetal film must be kept below some critical value J_(c). The value J_(c)varies according to the type of metal, the method of deposition, and thelocal environment. Mathematically,

J<J_(c)   (8)

[0058] J_(c) may be on the order of 10⁶ A/cm². The amount of AC currentthat will flow in the varactor is a function of the RF voltage andimpedance. If the peak AC voltage swing is denoted by V_(max), the peakAC current is

I_(max)=jωCV_(max)   (9)

[0059] For the cell of FIG. 3, Eqn. 9 implies the following inequalitiesfor the top and bottom electrodes, respectively $\begin{matrix}\begin{matrix}{\frac{I_{\max}}{t_{c}W} < J_{c}} & \quad & \quad & {\frac{I_{\max}}{t_{b}( {{2L} + W} )} < J_{c}}\end{matrix} & (10)\end{matrix}$

[0060] where t_(c) and t_(b) are the thicknesses of the top electrode140 and bottom electrode layer 112, respectively.

[0061] According to the first inequality in Eqn. 10, the width W mustsatisfy $\begin{matrix}{{W > W_{\min}} = \frac{I_{\max}}{t_{c}J_{c}}} & (11)\end{matrix}$

[0062] The constraint on length L is slightly more complicated since thecurrent density in the bottom contact is set by the quantity (2L+W), andalso since the length-width product LW=A is set by the desiredcapacitance value of the cell. Substituting W=A/L in the secondinequality in Eqn. 10 and then manipulating results in $\begin{matrix}{{{2L} + \frac{A}{L} - \frac{I_{\max}}{t_{b}J_{c}}} > 0} & (12)\end{matrix}$

[0063] This inequality will be satisfied by large values of L (in whichcase the 2L term is large) or for small values of L (in which case theA/L term is large). However, the small value solutions typically areless interesting because they represent the case where two short sidesand one long side of a rectangular cell are current conducting (i.e.,the case where L in FIG. 4C is small and W is large). A valid celldesign has values of W and L that satisfy Eqns. 11 and 12 as well as theequality LW=A, where A is set by the desired capacitance of the cell.There is no guarantee that a valid cell design exists.

[0064] The quantity on the left in Eqn. 12 can be thought of as the“excess” current conducting perimeter beyond what is needed to keep thecurrent density in the bottom electrode below the threshold currentdensity. It is a measure of how close to the current handling limit thevaractor design is. The larger the quantity, the farther away from thelimit is the design. There is no guarantee that there is a realizablelength in the range L<L_(max)=A/W_(min) that will satisfy Eqn. 12. Ifthere is not, one possible solution is to increase the metal thicknessesuntil a realizable design is achieved. However, the bottom electrodelayer 112 is typically made from an expensive refractory material suchas platinum. Hence, it is desirable to minimize the electrode thicknessin order to reduce the amount of expensive metal required. It is alsodesirable to keep this thickness small in order to avoid lithographyproblems resulting from non-planar topology.

[0065] Hence, the approach described above is an attractive alternatesolution. That is, the current density can be reduced by increasing thecurrent conducting perimeter of the active region, while maintaining thesame area. One way to do this is to increase the number of cells. Ifthere are N cells, then the area and peak current in each cell isreduced by 1/N. Therefore, Eqn. 12 becomes $\begin{matrix}{{{2L} + \frac{A}{NL} - \frac{I_{\max}}{t_{b}J_{c}N}} > 0} & (13)\end{matrix}$

[0066]FIGS. 7A and 7B are graphs of excess current conducting perimeter(i.e., the lefthand side of Eqn. 13) as a function of length L for N=1and N=4 cells, respectively. These graphs are plotted only for values ofL which satisfy the inequality L<L_(max)=A/W_(min). In other words, thegraphs plot the excess current conducting perimeter only for allowablevalues of stripe length L. In order to be a valid cell design, theexcess perimeter must be greater than zero (Eqn. 13) and the resultingcell design must also have acceptable resistive loss (generally, lowerresistive losses are achieved by higher values of L, as discussedpreviously). In FIG. 7A, the only values of L which satisfy Eqn. 13 arelow values of L, but these probably have unacceptable resistive loss.Thus, it is likely that an acceptable 1-cell design does not exist. InFIG. 7B, larger stripe lengths also satisfy Eqn. 13, suggesting that avalid 4-cell design likely does exist.

[0067] Although the invention has been described in considerable detailwith reference to certain preferred embodiments thereof, otherembodiments will be apparent. For example, the shapes of the top andbottom electrodes in FIG. 3 could be switched. As another example, theelectrodes and active regions can take shapes other than rectangular,for example circular, semicircular or serpentine. In these cases, thedesign objective of increasing perimeter would still favor the use ofmultiple cells, but the exact resistive model and design equations wouldbe different than those presented herein although the principlesillustrated would still be applicable. As a final example, it is notnecessary that all cells have exactly the same size and shape. A mix ofcells of different dimensions and/or shapes could also be used toincrease the varactor perimeter. Therefore, the scope of the appendedclaims should not be limited to the description of the preferredembodiments contained herein.

What is claimed is:
 1. A parallel plate varactor comprising: a bottomelectrode; a top electrode; a dielectric layer sandwiched between thebottom electrode and the top electrode, wherein a permittivity of thedielectric layer varies according to an electric field applied to thedielectric layer; the bottom electrode, dielectric layer, and topelectrode are integrated on a substrate; and an overlap between thebottom electrode, dielectric layer, and top electrode defines an activeregion for the varactor; and wherein, for at least one of theelectrodes: a resistance of the active region of the electrode issignificantly higher than a resistance of a bulk region of theelectrode; the active region has a lateral area A, the electrode has acurrent conducting perimeter P; and a ratio R of the perimeter P to asquare root of the area A is at least 2.0.